Created
June 28, 2011 15:02
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Using logarithms to do hypergeometric tests with large N
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from math import log, exp | |
from mpmath import loggamma | |
def logchoose(ni, ki): | |
try: | |
lgn1 = loggamma(ni+1) | |
lgk1 = loggamma(ki+1) | |
lgnk1 = loggamma(ni-ki+1) | |
except ValueError: | |
#print ni,ki | |
raise ValueError | |
return lgn1 - (lgnk1 + lgk1) | |
def gauss_hypergeom(X, n, m, N): | |
"""Returns the probability of drawing X successes of m marked items | |
in n draws from a bin of N total items.""" | |
assert N >= m, 'Number of items %i must be larger than the number of marked items %i' % (N, m) | |
assert m >= X, 'Number of marked items %i must be larger than the number of sucesses %i' % (m, X) | |
assert n >= X, 'Number of draws %i must be larger than the number of sucesses %i' % (n, X) | |
assert N >= n, 'Number of draws %i must be smaller than the total number of items %i' % (n, N) | |
r1 = logchoose(m, X) | |
try: | |
r2 = logchoose(N-m, n-X) | |
except ValueError: | |
return 0 | |
r3 = logchoose(N,n) | |
return exp(r1 + r2 - r3) | |
def hypergeo_cdf(X, n, m, N): | |
assert N >= m, 'Number of items %i must be larger than the number of marked items %i' % (N, m) | |
assert m >= X, 'Number of marked items %i must be larger than the number of sucesses %i' % (m, X) | |
assert n >= X, 'Number of draws %i must be larger than the number of sucesses %i' % (n, X) | |
assert N >= n, 'Number of draws %i must be smaller than the total number of items %i' % (n, N) | |
assert N-m >= n-X, 'There are more failures %i than unmarked items %i' % (N-m, n-X) | |
s = 0 | |
for i in range(1, X+1): | |
s += max(gauss_hypergeom(i, n, m, N), 0.0) | |
return min(max(s,0.0), 1) |
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